Subgroups — C₃⋊#6029 #10597071

Order 600.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅²	C₂	1	1	yes	maximal, characteristic
2	#6029	—	3	1	no	maximal, Hall
3	C₂×C₃×C₅²	C₄	1	1	yes	characteristic
4	C₃⋊#168	—	5	6	no	maximal
5	C₄×C₅²	D₃	1	1	yes	characteristic
6	C₃×C₅²	C₈	1	1	yes	characteristic, complemented, Hall
7	C₃×C₄×C₅	D₅	1	6	yes	—
8	C₂×C₅²	Dic₃	1	1	yes	characteristic
9	#168	—	15	6	no	—
10	C₂×C₃×C₅	Dic₅	1	6	yes	—
11	C₅²	C₃⋊C₈	1	1	yes	characteristic, complemented, Sylow
12	C₃⋊C₈	—	25	1	no	Hall
13	C₄×C₅	D₁₅	1	6	yes	—
14	C₃×C₅	#168	1	6	yes	complemented
15	C₃×C₄	C₅⋊D₅	1	1	yes	characteristic
16	C₂×C₅	Dic₁₅	1	6	yes	—
17	C₈	—	75	1	no	Sylow
18	C₂×C₃	#1039	1	1	yes	characteristic
19	C₅	C₃⋊#168	1	6	yes	complemented
20	C₄	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
21	C₃	#6029	1	1	yes	characteristic, complemented, Sylow
22	C₂	C₃⋊#1039	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	C₃⋊(C₅⋊D₅)
commutator, hypocenter	C₃×C₅²	C₈
Fitting, cosocle	C₃×C₄×C₅²	C₂
socle, prime radical	C₂×C₃×C₅²	C₄
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₄

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.